For a Hermetian operator A, * (x)[A (x)] dx = (x)[A (x)] * dx. Assume
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For a Hermetian operator Aˆ, ∫ψ*(x)[Aˆψ (x)] dx = ∫ψ (x)[Aˆψ (x)]*dx. Assume that Aˆ f (x) = (a + ib) f (x), where a and b are constants. Show that if Aˆ is a Hermetian operator, b = 0 so that the eigenvalues of f (x) are real.
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